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A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute
CESifo Conference Centre, Munich
Area Conferences 2012
CESifo Area Conference on
Global Economy
25 – 26 May
A Factor Augmentation Formulation of the
Value of International Trade
Daniel M. Bernhofen and John C. Brown
CESifo GmbH · Poschingerstr. 5 · 81679 Munich, Germany
Tel.: +49 (0) 89 92 24 - 14 10 · Fax: +49 (0) 89 92 24 - 14 09
E-mail: [email protected] · www.CESifo.org
A factor augmentation formulation of the value of international trade1
Daniel M. Bernhofen
University of Nottingham, CESifo and GEP
and
John C. Brown
Clark University and GEP
May 10, 20122
Abstract
Following Samuelson‟s seminal 1939 contribution, existing formulations of the aggregate gains
from trade are rooted in the theory of consumer demand. Their empirical implementation requires either
aggregate consumption data, which are rarely available, or are based on specific functional forms on the
utility of a representative consumer. We propose a normative assessment of the value of international
trade which is rooted in production theory and which is a generalization of Ricardo‟s 1817 formulation of
the gains from trade. In our formulation an economy‟s opportunity to trade is valued by a relaxation of its
endowment constraints. We show that the economy‟s factor content of trade serves as a sufficient statistic
for a factor augmentation equivalent to trade. An advantage of our formulation is that it imposes no
restrictive assumptions on consumer behaviour and requires only data observed in a trade equilibrium.
Applying our formulation to a high quality data set on product and task-specific factor employments in
19th century Japan, we are able to answer the following counterfactual: What factor augmentation would
have been necessary to compensate the economy for an overnight suspension of trade in its early trade
years of 1865-1876? We find that trade was, on a yearly average, revealed to be equivalent to a 7%
increase in Japan's female labour force, a 3% increase in its male labour force and a 3% increase in its
cultivated land.
JEL classification: F11, F14, N10, N75.
Key words: gains from trade, factor augmentation equivalent to trade, 19th century Japan.
1
Address for Correspondence: Daniel Bernhofen, School of Economics, University of Nottingham and GEP,
University Park, Nottingham, NG7 2 RD, UK. Tel: 44 115 846 7055, Fax: 44 115 951 4159, email:
[email protected] .
2
We acknowledge financial support from the National Science Foundation Grant SES-0452991 and the Leverhulme
Trust Grant F/00 114/AM. Shōji Masahiro provided excellent research assistance. Earlier versions of this paper
were presented at the 2010 AEA Cliometrics session in Atlanta , 2011 ETSG in Copenhagen and seminars at Bank
of Japan, City University of New York, Hitotsubashi University, London School of Economics, Keio University,
National University of Ireland at Maynooth, Osaka University and the University of Nottingham. We benefitted
from comments by Ray Chetty, Arnaud Costinot, Dave Donaldson, John McLaren, Kris Mitchener, Peter Neary,
Wolfgang Keller and Alan Woodland.
1
1. Introduction
The argument about the benefits of international trade is one of the oldest questions in economics.
And since the argument is also closely related to whether competitive market forces allocate resources in
the „right direction‟, it is also at the core of our discipline. Three fundamental questions arise: How does
one value an economy‟s trade? Does trade have a positive value to the economy? Since we almost never
observe a market economy in the absence of international trade, how can we empirically construct a
counterfactual statement about the value of international trade? Since our paper makes some progress on
all three questions, we use them as an organizing principle to highlight our contributions.
We suggest a factor augmentation formulation of the gains from trade in which an economy‟s
factor content of trade serves as a sufficient statistic for causal inference about the existence, magnitude
and sources of the gains from trade. The central idea is that an economy‟s factor content of trade reveals
information about the augmentation of resources that would be necessary for the economy to attain free
trade consumption with domestic production in a„trade- equivalent autarky equilibrium‟.3 An attractive
feature of this formulation is that it imposes no restrictive assumptions on consumer behaviour and does
not require data on the economy‟s actual autarky equilibrium. Applying our framework to a unique
historical data set on product and task-specific factor employments of 19th century Japan, we provide
causal evidence of gains from trade which are characterized by an augmentation of all factors of
production. We are also able to answer the following counterfactual: What factor augmentation would
have been necessary to compensate the economy for an overnight suspension of trade during the period of
3
The concept of an „equivalent autarky equilibrium‟ (denoted without the prefix „trade‟) goes back to Deardorff and
Staiger (1988), who show that the factor content of trade can be used to examine the effects of trade on factor prices.
Deardorff (2000) provides a generalization. More recently, Burstein and Vogel (2011) extend this framework to
imperfect competition and heterogeneous firms. However, none of these papers link the factor content of trade to the
aggregate gains from trade.
2
1865-1876? A careful construction of the economy‟s factor content of trade reveals that the benefit of
trade, was on a yearly average, equivalent to a 7% increase in Japan‟s female labour force, a 3% increase
in its male labour force and a 3% increase in its cultivated land.
Our gains from trade characterization can be viewed as a modern formulation of what Jacob
Viner (1937, p. 440) has famously called the 18th century rule for the gains from trade: “…it pays to
import commodities from abroad whenever they can be obtained in exchange for exports at a smaller real
cost than their production at home would entail.” Recognizing that the „real costs‟ of goods are the
resources embodied in them, international trade can be viewed as an exchange of factor services within a
cost-benefit framework. The costs from trade are the resources embodied in a country‟s total exports; the
benefits from trade are the counterfactual resources that would have been required to produce the foreign
imports domestically. We will illustrate that David Ricardo used this cost-benefit perspective of the gains
from trade in his famous 1817 paragraph on comparative advantage. Hence, our gains from trade
characterization can be viewed as generalizing David Ricardo's labour value formulation of the gains
from trade to the case of multiple factors. From an empirical perspective, this formulation is attractive
since the data could reveal that the costs of exports exceed the benefits from imports, allowing for the
empirical possibility that competitive markets allocate resources in the wrong direction. In other words,
the gains from trade become an empirically refutable proposition, rather than a theoretical assumption.
Existing characterizations of the gains from trade are rooted in classical consumer utility or
revealed preference theory. However recent research in behavioural economics has accumulated a large
body of evidence questioning the conventional assumptions about preference satisfaction.4 In light of this
evidence, it appears to be desirable to have a normative formulation of the gains from trade which does
not depend on strong preference assumptions of a representative consumer. We suggest a normative
4
See Sugden (2004)for a summary of the empirical evidence against rationality-based models and the problems it
creates for welfare analysis. Three prominent issues are: (i) random variation of preferences, (ii) referencedependent preferences and (iii) shaping effects in subjective valuations.
3
assessment where the value of international trade is not cast in terms of a change in preference
satisfaction but rather by a change in the endowment constraints that the economy faces.5 Since an
economy‟s factor content of trade embodies all the relevant information about the corresponding resource
inflows and outflows, it serves as a sufficient statistic for a precise welfare statement without imposing
any restrictions on the demand side of the economy.6 From a formal general equilibrium perspective, the
factor content reveals information about a trade- equivalent autarky equilibrium, which is defined as an
autarky equilibrium constructed by augmenting factor endowments such that free trade consumption can
be obtained by domestic production.
Our formulation is quite general by not imposing any structure on the specific mechanism
generating international trade. Instead, the economy‟s factor content is indicative of the underlying
determinants of trade. If trade is governed primarily by endowment differences, as suggested by the
Heckscher-Ohlin model, the factor content of trade should reveal a factor trade-off: the economy
experiences an increase in some factors at the cost of giving up some others. On the other hand, a factor
augmentation which is characterized by an increase in all factors suggests a role for technological
differences. The nature of the factor augmentation will determine how the gains from trade can be
formulated. For example, if the factor content of trade reveals an augmentation in all factors, the value of
trade can be expressed in terms of an overall expansion of the economy‟ endowment vector and the
existence and magnitude of the gains can be uniquely determined without reference to any factor
5
On a fundamental level, our welfare criteria emphasizes the expansion of choices that result from relaxing the
economy‟s aggregate endowment constraints. Our approach is reminiscent of Bernheim and Rangel (2007,2009),
who suggest normative frameworks that are rooted in the freedom of choice, but do not require coherence of
preferences.
6
Chetty (2009) provides an excellent survey of the 'sufficient statistic approach' for welfare statements in the public
economics literature. We are aware of two applications in the trade literature. Arkolakis, Costinot et al. (2009)
identify two macro-level 'sufficient statistics' to estimate the gains from trade under different model specifications.
However, these estimates are based on strong symmetry assumptions and functional forms on consumer utility and
import demand systems. Bernhofen and Brown (2005) use autarky goods prices as a sufficient statistic for
estimating comparative advantage gains from trade. But the latter paper also requires the assumption of a
representative consumer who follows the weak axiom of revealed preferences.
4
valuation. In the case of a factor trade-off, a factor valuation is required to establish both the existence and
the magnitude of the gains from trade.
We introduce factor income equivalent and compensating measures of the gains from trade which
can be thought of as duals to the well-known Slutsky expenditure measures of the gains from trade. We
show that our factor income equivalent measure is an upper bound to the corresponding Slutsky
equivalent variation measure and that our factor income compensating measure is a lower bound to the
corresponding Slutsky compensating variation measure of the gains from trade. In addition, our factor
augmentation formulation of the value of international trade can be expressed in terms of the resource
inefficiency of the economy‟s autarky equilibrium relative to its trade-equivalent-autarky equilibrium.
The degree of inefficiency can be quantified by Debreu‟s (1951) coefficient of resource utilization, where
the loss of resource utilization stems from the inefficiency of economic organization resulting from the
imposition of prohibitive import tariffs cutting off all international trade.7
Since our framework requires only data on factor prices and an economy‟s factor content of trade
it has the potential for a broad domain of empirical applications. In this paper, we apply it to a high
quality data set on product-specific factor employments in 19th century Japan. There are several attractive
features of our empirical setting. As argued in Bernhofen and Brown (2004, (2005), the Japanese
economy shortly after its opening falls in the domain of a neoclassical economy producing relatively
homogeneous products characterized by perfect competition. Because of the limited technological
change during the first decades after the economy's opening up, we can justifiably calculate and trace the
economy's factor content of trade during a 10+ year “experimental window'” that employs a single factor
employment matrix. In addition, since Japan by-and-large imported goods that were very close substitutes
to domestically produced goods, we are able to calculate the factor requirements that would have been
7
Although Debreu (1951, p. 286) mentions a potential application of his resource utilization measure for an
economy that applies a system of tariffs, we are not aware of any paper applying his measure to the gains from trade.
5
necessary to produce the imported goods with domestic production techniques. The factor content of trade
is constructed from detailed historical data – much of it at the task level- on the direct and indirect
domestic input requirements of Japan‟s tradables. The construction of the technology matrix draws upon
numerous historical sources, including a major Japanese survey of agricultural techniques and a rich set of
comparative cost studies. The detail available on technologies allows for a close assignment of factor
usage to each commodity and also accounts for any significant trade in intermediate goods.
A further advantage of applying our factor augmentation formulation to the case of Japan is that
the ability to observe factor prices under both autarky and free trade allows for a complete empirical
exploration of the different formulations of the gains from trade. Exploiting autarky goods prices,
Bernhofen and Brown (2005) have shown that the consumption equivalent variation measure of the gains
from trade was approximately 9% of Japan‟s GDP at the time. Evaluating the factor augmentation at both
autarky and free trade factor prices we find that our factor income equivalent and compensation measures
result in quite comparable average magnitude over the time period of 1865 to 1876. Specifically, we
show that the suspension of trade is equivalent to an average loss of resource utilization of about 8%.
Given that the gains from trade estimates in Bernhofen and Brown (2005) assume that consumer
behaviour, in the aggregate, follows the weak axiom of revealed preference, whereas the current paper
does not make this assumption, our „equivalence findings‟ can be interpreted as providing indirect
empirical support for the empirical validity of this axiom.
2. Conceptualizing the benefits from trade
To put our characterization of the welfare effects of trade into perspective, we start out by briefly
reviewing the existing consumer based measures of the gains from trade. We then introduce our factor
content characterization in its different settings.
2.1 Samuelson’s gains from trade formulation
6
Our current neoclassical characterization of the gains from trade is rooted in Samuelson‟s seminal
1939 paper. In that paper Samuelson theoretically proved the existence of the gains from trade and also
linked the gains from trade characterization to the weak axiom of revealed preference.8 Since then the
standard characterization of the gains from trade involves a welfare comparison of the consumption level
of a representative consumer under autarky and trade.9
Consider a small competitive economy that produces the same n goods under autarky and trade.
The autarky equilibrium is characterized by an n-vector of autarky prices pa and an n-vector of
consumption Ca. The free trade equilibrium is given by n-vectors of prices pt and consumption Ct.
Samuelson (1939) showed that competitive producer behaviour and balanced trade imply that ptCt≥ptCa.
The consumption welfare measures of the gains from trade can then be thought of as capturing “the
distance” between Ca and Ct in expenditure equivalents. Using free trade prices pt as the evaluation
criterion gives the Slutsky compensating variation measure of the gains from trade:
ΔICV = ptCt-ptCa.
(1)
ΔICV is interpreted as the change in income necessary to compensate the representative consumer for the
suspension of trade. Alternatively, using autarky prices pa as the evaluation criteria, one obtains the
Slutsky equivalent variation measure of the gains from trade:
ΔIEV= paCt-paCa.
(2)
Taking autarky at the reference point, ΔIEV is the change in income that would enable the representative
consumer to attain the free trade consumption bundle at autarky prices. While the sign of (1) follows from
8
Samuelson (1939)‟s gains from trade article follows up on Samuelson (1938), which introduces the concept of the
weak axiom of revealed preference. This axiom allows for the formulation of the theory of demand without relying
on the concept of utility. Subsequent papers by Samuelson (1962) and Kemp (1962) extend the gains from trade
argument to the case where an economy is large enough to influence the terms of trade.
9
By taking consumption as the primitive, we focus on the revealed preference approach to consumer demand which
corresponds to the Slutsky income characterization of a welfare change. Alternatively, one could take utility as the
primitive which corresponds to the Hicksian income characterization of a change in welfare.
7
optimizing behaviour, the sign of (2) follows from (1) and the assumption that consumer behaviour, in the
aggregate, follows the weak axiom of revealed preference.
[insert Figure 1 here]
Figure 1 illustrates both measures. Since (1) and (2) require aggregate consumption data under both
autarky and trade, which are usually not available, they are difficult to implement empirically.10
However, if data on autarky goods prices are available, Bernhofen and Brown (2005) have shown that the
economy‟s net import vector evaluated at autarky prices provides an upper bound for the Slutsky
equivalent variation measure (2). Applying this logic to autarky prices and data flows for 19th century
Japan, they find upper bounds on the gains from trade of about 8 to 9 percent of GDP.
2.2 A factor augmentation equivalent to trade
The Slutsky compensation measures (1) and (2) use goods prices as metrics to capture the
distance between the autarky and free trade consumption vectors Ca and Ct, as illustrated in Figure 1.
Alternatively, instead of focusing on income changes to afford consumption levels, we can compare the
resources necessary to produce the autarky and free trade consumption vectors Ca and Ct.
Assume the economy is able to produce the n goods from k primary factors of production. The kvector of the economy's factor endowments is denoted by L. The economy‟s domestic technology under
trade is given by an n x k matrix A, where an entry aij denotes the number of units of factor i necessary to
produce one unit of good j.11 Full employment implies then that L=AYt, where Yt is the n-vector of
production in the trade equilibrium. International trade enables the economy to separate consumption
10
The general lack of output data also prevents one to infer consumption from output and trade data.
11
Unless technologies are characterized by fixed input coefficients, the unit input requirements will depend on
factor prices. In our notation A are the optimal techniques in the trade equilibrium and we suppress the dependence
on factor prices.
8
from production, with the difference being the economy‟s net import vector, defined as T=Ct-Yt. The kvector of factor prices in the trade equilibrium is denoted by wt.
Starting from the economy‟s trade equilibrium, we can consider the following counterfactual.
Assuming trade were suspended, by how much would the economy‟s endowment vector have to be
augmented for the economy to produce the consumption vector Ct with its own domestic production
techniques? Obviously, the augmented endowment vector Laug is given by Laug=ACt, which implies that
the corresponding augmentation of resources must be ΔL=Laug-L. A great advantage of this formulation is
that the factor augmentation is revealed by the domestic factor content of the economy‟s net import
vector, which follows from ΔL=Laug-L=ACt-AYt=AT.
Let us now split the economy's net import vector T into its individual components, where M
denotes the vector of imports and X the vector of exports. Accordingly, the domestic technology matrix
can then be written as A=(Am,Ax), where Am is the matrix of domestic input requirements of imports and
Ax is the matrix of domestic input requirements of exports. The „factor augmentation equivalent to trade‟
can then be written as:
ΔL=Laug-L=AmM-AxX
(3)
Intuitively, (3) conceptualizes the gains from international trade in terms of a cost-benefit
framework. Exports are the costs of international trade since they result in resource outflows that are
captured by the factor content of exports, defined as AxX. Imports are the gross benefits from trade.
Under the assumption that the import vector M could have been produced with domestic technologies, the
gross benefits from trade are the counterfactual resources that would have been necessary to produce the
imported goods domestically, which is the vector AmM. The resulting net benefit from trade is then
simply AmM-AxX. Trade is equivalent to augmenting the domestic endowment vector from L to
Laug=L+AmM-AxX.
[insert Figure 2 here]
9
So far we have only demonstrated that Ct is feasible to produce with the augmented endowment
vector Laug . Now we establish that Ct can be the production outcome of a competitive equilibrium. We
proceed by introducing the concept of a trade-equivalent autarky equilibrium:
Definition: A trade-equivalent autarky equilibrium is an equilibrium that would arise if trade
were suspended, but if the economy‟s endowment vector were augmented to Laug =L+AmM-AxX.
Given a trading equilibrium where the economy is incompletely specialized, Deardorff and
Staiger (1988) have shown that a trade-equivalent autarky equilibrium exists such that the economy's
augmented endowment vector Laug will produce the free trade consumption vector Ct with domestic
technologies and the same goods and factor prices pt and wt as in the trade equilibrium.12 Figure 2 depicts
the autarky equilibrium, the trade equilibrium and the trade-equivalent autarky equilibrium in a single
diagram. Factor augmentation results in production possibilities that are associated with an augmented
production possibilities frontier (PPF), denoted by PPF(Laug). In the trade-equivalent autarky
equilibrium, consumption coincides with production Ct and is tangent to pt on the augmented PPF(Laug).
The resource augmentation formulation exploits the fact that the economy‟s trade vector (X1 ,M2)
evaluated at the corresponding factor input requirements contains all the relevant information about the
difference between the resources embodied in Ct and Yt. The factor content of trade can be thought of as
a sufficient statistic for a factor augmentation equivalent to trade with the great empirical virtue that the
construction of this sufficient statistic requires only data that are observed in the trade equilibrium.
2.3 Ricardo's 1817 formulation of the gains from trade
Our cost-benefit characterization of the gains from trade (3) can be viewed as a formalization of
the 18th century rule of the gains from trade: “…it pays to import commodities from abroad whenever
12
The proof requires two parts. We have already shown the first part, which is that Ct is feasible to produce. Second,
it requires that Ct maximizes profits. For the proof of the second part we refer the reader to Deardorff and Staiger
(1988), p. 96 equations (2.8) and (2.9), since a replication would require us to introduce additional notation.
10
they can be obtained in exchange for exports at a smaller real cost than their production at home would
entail “ (Viner, 1937, p.440). In a recent paper, the historian of economic thought Andrea Maneschi
(2004) has argued that David Ricardo followed this 18th century rule in his expression of the gains from
trade in his famous 1817 passage which discusses the trade in cloth between Portugal and England. This
passage employs what Samuelson (1969) so vividly labelled “Ricardo‟s four magic numbers” (where the
numbers are given in italics):
“England may be so circumstanced, that to produce the cloth may require the labour of
100 men if she attempted to make the wine, it might require the labour of 120 men for the
same time. England would therefore find it her interest to import wine, and to purchase it
by the exportation of cloth. To produce the wine in Portugal, might require only the
labour of 80 men for one year, and to produce the cloth in the same country, might
require the labour of 90 men for the same time. It would therefore be advantageous for
her to export wine in exchange for cloth. (Ricardo (1817, p. 82))”
Following John Stuart Mill‟s interpretation, trade theorists have interpreted Ricardo‟s four
numbers as unit labour coefficients: the amount of labour required in each country to produce one unit of
cloth or wine. More recent appraisals of this interpretation emphasize that it suffers from a serious
shortcoming: it is inconsistent with Ricardo‟s explication. At the outset, Ricardo introduces the first two
numbers and then uses them to infer England‟s pattern and gains from trade without reference to the third
and fourth numbers. If these were unit labour coefficients, the logic of the argument would require
information on all four numbers before Ricardo could state a conclusion about the pattern of England‟s
(and Portugal‟s) trade.
Drawing upon earlier work by Sraffa (1930), Ruffin (2002) and Maneschi (2004) suggest that
Ricardo‟s four numbers pertain to the amount of labour embodied in each country‟s exports and imports
11
rather than unit labour coefficients.13 In light of this interpretation, Ricardo‟s gains from trade
formulation is a special case of (3). If labour is the only factor, ΔL becomes a scalar and can be thought
as a ”labour growth equivalent to trade.” Applying Ricardo‟s passage to Figure 2, assume that England
exports X1 units of cloth and imports M2 units of wine.14 Ricardo‟s assertion that “the cloth may require
the labour of 100 men” implies that 100=a1E X1 and his assertion that “if she attempted to make the wine,
it might require the labour of 120 men“ implies that 120=a2EM2. England‟s gains from trade can then be
expressed as ΔLE = a2EM2 - a1EX1 =120-100 or, as Sraffa (1930, p. 54) put it, England “gains the labour
of 20 Englishmen.” Analogously, Portugal‟s gains from trade can be written as ΔLP = a1PX1 - a2PM2 =9080 and “Portugal gains the labour of 10 Portuguese” ( see Sraffa (1930, p. 54)).15 Given the four data
points in Ricardo‟s famous paragraph, Sraffa proposes that Ricardo measures the welfare benefits from
trade with an increase of 20 workers in England and an increase of 10 workers in Portugal.
2.4 Measuring the benefits of the factor augmentation
In the Ricardian model, the factor augmentation equivalent is a scalar and the gains can be
expressed in the growth of a single factor. In a world with more than two factors, the factor content of
trade will reveal whether a metric is required to express the value of international trade. Figure 3
illustrates the two-factor case where the economy's endowment vector L partitions the endowment space
into four quadrants: I, II, III and IV. If Laug is revealed to fall either in quadrant I or III, the existence
and the composition of the gains (or losses) from trade can be expressed without the need of a metric. For
example, if Laug falls into quadrant I, the economy gains in both factors and the gain ΔLi of any factor i
can be expressed as a percentage increase in the economy‟s endowment Li,. similar to the one-factor
model discussed in the previous section. However, the factor content provides now additional information
13
Bernhofen (2009) argues further that the labour content interpretation yields a pattern of trade prediction which
restores coherence to this famous passage and is also compatible with Ricardo‟s labour theory of value.
14
15
In what follows, superscripts E and P on input coefficients and endowments pertain to England and Portugal.
If the terms of trade is such that X1=M2=1, then Sraffa's and Mill's interpretations coincide.
12
on the sources of the gains with regard to the individual factors. On the other hand if Laug falls into
quadrant III, the economy‟s factor content reveals losses from trade in terms of all factors. Economic
theory predicts that this could occur through terms of trade affects or government induced distortions.
Since the factor content of trade could reveal that trade takes an economy into quadrant III, the gains from
trade become an empirically refutable proposition. However, if Laug falls either in quadrant II or IV, the
factor content reveals a factor trade-off which suggests a strong role of Heckscher-Ohlin forces as a
source of trade. However, the existence and magnitude of the benefit of the factor augmentation can only
be established by applying some metric to evaluate the factor trade-off.
[insert Figure 3 here]
Recall from (3) that Laug is constructed by adding the resources that would have been necessary
to produce the economy‟s import vector counterfactually at home, AmM, and subtracting the resources
embodied in the economy‟s export vector AxX. The welfare effects of trade can then be analyzed by
comparing the economy‟s autarky equilibrium (L,Ca,wa,pa) with its trade-equivalent autarky equilibrium
(Laug,Ct,wt,pt). 16 Specifically, the two equilibria can be compared with respect to the corresponding
resource constraints L and Laug. Recognizing that a competitive equilibrium can be replicated by a
constrained optimization problem in which the social planner faces the resource constraints L and Laug ,
the economy's corresponding factor price vectors wa and wt constitute the shadow prices at which the
planner evaluates any changes in the economy's resource constraints. Starting from the autarky
equilibrium, the social planner will view a change in the resource constraint from L to Laug as beneficial
only if wa(AmM)>wa(AxX) with the net gain from the resource exchange being wa(AmM)-wa(Ax X).17 We
can now define a dual to the Slutsky equivalent variation measure (2), which is the increase in factor
16
The k-vectors wa and wt are factor prices in the autarky and trade equilibrium, respectively.
17
An attractive feature of the shadow price interpretation associated with changes in the resource constraints is that
social welfare gains can be expressed without knowledge of the consumption objectives of the society (see Dixit
(1990), p.43).
13
income that would be equivalent to obtaining the augmented endowment point Laug at the autarky factor
prices wa. This factor income equivalent measure, denoted by ΔLEV, is given by:
ΔLEV= waLaug -waL = wa(AmM)-wa(AxX).
(4)
Alternatively, starting from the trade-equivalent autarky equilibrium, the social planner will view
a change in the resource constraint from Laug to L as a loss only if wt(AmM)>wt(AxX) with the net loss
being wt(AmM)-wt(Ax X). Accordingly, we can define a dual to the Slutsky compensating measure (1),
which is the change in factor income which would compensate the social planner from being forced to
change the available resources from Laug to L. We define this as compensating measure of the benefit of
the endowment augmentation and denote it by ΔLCV:
ΔLCV= wtLaug -wtL = wt(AmM)-wt(AxX).
(5)
Figure 3 provides a graphical illustration of (4) and (5) by drawing parallel lines through L and
Laug with the slope of (-w1j/w2j), (j=a, t). The horizontal distance between the lines measures the benefits
of the augmentation in units of factor 1.
The factor income measures (4) and (5) can also be quantitatively linked to the Slutsky
expenditure measures (1) and (2). The relationship between the factor income equivalent measure ΔLEV
and the Slutsky equivalent variation measure ΔIEV is summarized in the following proposition:
Proposition 1: Assuming that producers maximize profits and consumption conforms to the weak
axiom of revealed preference, then ΔLEV≥ ΔIEV>0
14
Proof:18 From Samuelson (1939) we know that profit maximization in conjunction with the weak axiom
of revealed preference implies that paCt > paCa. Recognizing that it is technologically feasible for the
economy to produce Ct from Laug, profit maximization in the autarky equilibrium implies that paCawaL≥paCt-waLaug. Rearrangement implies that waLaug-waL≥paCt-paCa>0.
Proposition 1 establishes that if there are gains from trade in the revealed preference sense then
the factor income measure (4) will always be positive and bigger than the Slutsky equivalent variation
measure. The intuition for the latter is that since the augmentation is evaluated at free trade factor prices,
it overestimates the endowments necessary to produce Ct by ignoring the resource savings from optimally
adjusting input coefficients to autarky factor prices. The relationship between the compensating measures
is captured in the next proposition:
Proposition 2: Assuming that producers maximize profits, then ΔICV≥ ΔLCV
Proof: Since it technologically feasible to produce Ca from L, profit maximization in the trade equivalent
autarky equilibrium implies that ptCt-wtLaug≥ptCa-wtL. A simple rearrangement yields then ptCt--ptCa≥
wtLaug-wtL.
Since the compensating variation measure (1) does not require the weak axiom of revealed
preference, Proposition 2 implies that the factor income compensating measure (5) provides a lower
bound without having to assume anything about consumer behaviour. A further advantage is that the
lower bound requires only data in the trade equilibrium.
If the magnitudes of (1) and (2) are not too different, the factor income measures (4) and (5) are
complementary by providing an upper and lower bound for the consumer based measures of the gains
from trade. Furthermore, if (4) and (5) are similar in magnitude, this could be interpreted as providing
evidence for validity of the weak axiom of revealed preference in the data set.
18
Formally, this proof replicates Deardorff (1982) who links the sign of (4) to a general Heckscher-Ohlin pattern of
trade prediction, whereas we argue that the magnitude of (4) is linked to the gains from trade.
15
The sub-optimality of autarky relative to trade can also be framed in context of Debreu‟s (1951)
coefficient of resource utilization.19 Taking the trade equilibrium as the reference point, the endowment
vector Laug corresponds to the economy‟s optimal utilization of resources. The suspension of trade can be
thought of lowering the economy‟s resource utilization to L. The difference vector Laug-L represents a
loss from „non-utilized‟ resources, which can be evaluated at either wa or wt.20 The inefficiency of L
relative to Laug can then be expressed by:
ρj = wjL/wjLaug ,
(j=a,t)
(6)
The coefficient ρj measures the distance between L and Laug in the metric of the equilibrium resource
prices wj (j=a,t,).21 It is a number between 0 and 1, with a smaller value suggesting a higher degree of
inefficiency of autarky relative to trade. If data on both autarky and free factor prices are available, the
coefficients provide a convenient metric to compare the relative magnitudes of (5) and (6) and, following
from Propositions 1 and 2, a unified approach to quantify the benefits from trade.
3. Empirical implementation
The opening up of Japan to international trade in 1859 after over two centuries of near autarky
provides an unusual opportunity to empirically implement the factor augmentation characterization of the
gains from trade in an environment where it can be compared to the autarky-based consumer expenditure
19
See Deaton (1979) for a discussion of Debreu‟s coefficient of resource utilization in context of a systematic
treatment of distance functions in welfare economics.
20
Since some components of (Laug-L) might be negative, „non-utilization‟ pertains, in a general equilibrium sense,
to the vector as a whole.
21
In Debreu's original formulation (see Debreu (1951)), ρ is defined on the economy's 'achievement level', which in
this case would be the aggregate utility level ut in the trade-equivalent autarky equilibrium. However, such a
formulation would require the introduction of trade and factor trade utility functions in the spirit of Woodland
(1980) and Neary and Schweinberger (1986). In terms of Figure 2, Laug could then be thought of lying on a factor
trade indifference curve with achievement level ut. Proposition 2 in Neary and Schweinberger (1986) shows that
such a factor trade indifference curve is well-behaved. However, we opted in (6) for a formulation which does not
require the assumption of an aggregate social welfare function.
16
measures reported in Bernhofen and Brown (2005). Bernhofen and Brown (2004, 2005) describe this
episode in detail. A central feature of the case of Japan is that during its early trading years of 1865-1876
the economy primarily imported goods with very close domestic substitutes. This allows us to calculate
the counterfactual domestic input requirements that would have been necessary to produce foreign
imports with domestic production techniques.
The implementation of our gains from trade formulations in section 2.4 requires data on trade
flows, domestic input requirements and factor prices. We restrict our analysis to the years 1865, 18671876. Although Japan officially opened up to trade on July 4, 1859, the government of Japan was able to
restrict the sale of its main exports (products of the sericulture industry) until western military
intervention ended these efforts in 1864. Complete trade records for 1866 are missing because of a fire in
the customs house of the main trading port, Yokohama. The last trading year chosen is well before
significant imports of western technology starting in the 1880s altered the Japanese technology matrix
that prevailed for the first period of open trade.
3.1 Data sources and variables
A data appendix available from the authors provides information on the historical sources
used to construct the vectors of exports X and imports M and the technology matrix for Japan.
The abundant documentation allows us to define the trading vector at the level of individual
products, or at a level of detail comparable to the most disaggregated level for contemporary
trade data. For example, ten per cent of Japan‟s imports were an unfinished lighter cotton cloth
known as gray shirtings. The sources note that almost all of the cloth was imported from Great
Britain and the most common weight was 8.25 lbs. for a piece with a length of 40 yards and a
width of 39 inches. The level of detail permits a close match between the elements of the
technology matrices and import and export vectors.
17
Our historical research on the production conditions of the Japanese economy suggests a
level of aggregation over five factors of production: three kinds of labor, land and capital. This
approach to defining factors was designed to capture two essential features of technologies of the
last third of the nineteenth century: the presence of a division of labour by sex and significant
cross-industry differences in the use of skilled labour.22 For that reason, our factor grouping uses
three categories of labour measured in days per unit of output: skilled male, unskilled male, and
x
female. For the A matrix of Japan‟s exports, workers on the farm were included among
unskilled workers. The category of skilled male workers includes production workers with
specialized skills (such as master smelters (murage) or tea sorters), master craftsmen such as
dyers or master miners and owner-operators of specialized small firms such as fishermen. The
fourth factor is capital, which is the user cost of capital measured in terms of gold ryō with the
purchasing power of 1854-1857.23 Capital costs took account of the relatively high rates of
depreciation of wooden tools and equipment and the high rates of interest that prevailed in Japan
during the test period.24 The final factor is land. To facilitate comparisons with Japanese sources,
land is measured in terms of tan, which is equivalent to one-tenth of a hectare or one-quarter of
an acre.25 All measured land is assumed to be useable as cropland, or its equivalent in Japan,
dryfield land.26
22
The data appendix provides a more detailed discussion of the rationale for and measurement of the five factors.
The gold ryō was the gold-based currency of Japan until it was replaced with the yen in 1871 at one-to-one. Yen
and ryō values for years other than 1854-1857 were deflated using the index of non-tradable goods found in Shinbo
(1978, Table 5-10).
24
See Saitō and Settsu (2006) for a review of the available evidence on interest rates, which places the range in 12 to
15 percent.
25
The final section of the data appendix discusses the treatment of land that was not used for dryfield crops such as
wheat, barley, cotton or legumes.
26
Japanese land consisted of dryfields, which were used for crops such as cotton, soybeans and indigo, and paddy
land, which was used for rice.
23
18
The compilation of the Ax matrix included 23 different products. About 80 per cent of
Japan‟s exports were concentrated in just three of these: raw silk, silkworm eggs and green tea.
The main source for the resource requirements for these exports is the exhaustive prefecture-byprefecture survey of agricultural production conditions from the late 1880s, the Nōjji Chōsa (see
Chō, Shōda et al. (1979)). Coal, copper, various maritime products, mushrooms, camphor and
vegetable wax accounted for almost all of the rest. The construction of the Ax matrix for these
products took account of two features of the division of labour in production systems: the locus
of most production in vertically disintegrated and non-specialized units, which were primarily
rural households linked together by local markets, and the extensive use of female labour for
particular tasks on the farm and a limited number of skilled craftsmen at key points in production
processes. Japanese and western sources provide ample documentation of all stages of
production processes, so that the resource requirements for key intermediate goods such as
mulberry leaves, fertilizer, coal, charcoal and lumber can be readily included in the calculation of
the net resource requirements. For example, one pound of raw silk, Japan‟s most important
export, required about 15 days of male labour and 4 days of female labour. Of this amount, most
of the male labour was required for raising mulberry leaves (one pound of raw silk requires 360
pounds of leaves). Three-quarters of the female labour was for reeling, and the remainder was for
raising the other intermediate products of silkworm eggs and cocoons. Since the sericulture
industry resulted in a number of joint products that could essentially be treated as waste, input
requirements were adjusted to assume that all output was of a high enough quality to be
exported.
The construction of the Am matrix followed the same procedure as was used for the Ax
matrix. Essentially, the Am matrix provides the Japanese technologies that could be used to
19
produce Japan‟s imported goods. The Nōji Chōsa provided source information for Japanese
technologies for producing imported agricultural goods such as indigo, rice, soybeans and
unrefined sugar. Historical studies of Japanese firms provide information on the refining stages
of products such as indigo and sugar. Several studies, most notably Tanimoto (1998), provide
detail on the stages of production and technologies used in the cotton textile industry.27 The
detailed reports of the American geologist Benjamin Smith Lyman (see Lyman (1879)) provide
comprehensive accounts of Japanese technologies for drilling and refining petroleum, mining,
smelting and metallurgy.
The one product that deserves particular mention is woolen and worsted cloth, which
accounted for 21 per cent of Japan‟s imports by value. Japan‟s topography does not lend itself to
the widespread grazing of sheep, so that prior to the 1880s, Japan did not produce any woolens.
Historians such as Tamura (2004) have established that imported woolens by and large
substituted for various kinds of silk in Japanese dress.28 A key import during the 1860s, camlets
(a moderate-weight worsted cloth), was used for belts and haori (outer jackets). Mousseline de
laine and other lightweight worsted or mixed cloths that came to dominate imports during the
1870s substituted for domestic silk cloths such as chirimen in the sewing of kiminos. To account
for the resources required by woolen imports, woolen and worsted cloths were grouped into three
categories by weight; the resources required to produce the same square yardage of similar silk
cloths were then calculated. The main sources for the requirements for silk cloths include Bavier
(1874), Porter and National Association of Manufacturers (U.S.) (1898) and Ichikawa (1996).
The three cloths were chirimen, habutai and hakata-obi.
27
The Am matrix was constructed to accommodate different cloth weights. It assumed that all imported finished
cloth was dyed using indigo dye.
28
The major exception s were the heavier woollen cloths that were used for military uniforms, the uniforms of some
government employees and the western dress that was sometimes worn by a small elite minority.
20
Finally, the vectors of factor prices wa and wt must meet two criteria. First, they must
take full account of potential differences in the two most important economic regions of Japan
during autarky and open trade: the Kinai in the west (centered on Kyoto and Osaka) and the
Kantō, centered on Edo (Tokyo) in the east. The estimates of wages for unskilled male workers
and females for both the autarky (ca. 1855) and open trade periods (ca. 1878) were derived from
Saitō (1998). Several other local industry studies provided supplementary data on wages for
skilled workers during both periods.29
The second criterion is to take account of the fact that land varied in quality and use and
by location. A tan of a dryfield of low quality would rent for a fraction of the rent of highestquality paddy land. Detailed land price and rent evidence that includes information on both
characteristics is available for several locations in the west and two locations in the east, which
allowed for the estimation of hedonic regressions. The average predicted rent from these
regressions for good quality dryfields in the west was up to 1.82 ryō per tan; it reflects the
productivity of land in the region that supplied most of Japan‟s raw cotton. Data on the average
productivity of land for Japan as a whole relative to the sample villages used in the hedonic
regressions were used to convert the predicted rents in the Kinai to an average rent of 1.04 ryō
for all of Japan.30 Data on land values for the open trade period becomes plentiful during the
1870s. Property transactions recorded in the Tokyo Journal of Economics (Tokyo Keizai zasshi)
provide coverage for much of Japan for paddy land. These rents are adjusted downwards by
about one-half to provide an estimate of rents for dry fields.31 Capital was the numéraire for the
29
Autarky day wages were 0.053, 0.027 and 0.019 ryō ca. 1855. Wages ca. 1878 were about 0.20, 0.15 and 0.11
yen.
30
Le Gendre (1878, Appendix Table) provides the data on productivity per tan for all of Japan‟s prefectures ca.
1874.
31
The rents are 1.04 ryō per tan (one-quarter acre) in the mid-1850s and 3.82 yen per tan in 1878.
21
autarky period (priced at one ryō). For the open trade period, the price of capital was inflated to
reflect the diminished purchasing power of the ryō by the mid-1870s. The price index for nontradable goods compiled by Shinbo (1978, Table 5-10) was used to arrive at a price of capital
that was 4.1 yen ca. 1878.
3.2 Japan’s revealed resource augmentation
Table 1 provides information on Japan‟s revealed resource augmentation ΔL from equation (3)
and its individual components for each sample year. Factor flows of the three types of labour are
measured in millions of days; capital is given in thousands of ryō; and land in thousands of tan. Panel A
gives the counterfactual resources necessary to produce Japan‟s imports domestically, AmM. Panel B
documents the resource outflows embodied in Japan‟s exports, AxX Panel C gives AmM-AxX, the factor
augmentation necessary to produce Japan‟s free trade consumption vector domestically in a tradeequivalent autarky equilibrium. A striking feature of Panel C is that the factor content reveals a factor
augmentation in each factor in each sample year. In terms of Figure 2, Japan‟s factor content of trade
reveals no factor trade-off, which implies that the endowment vector Laug always lies in quadrant I.
Since all components of (Laug-L) are positive in each sample year, Panel C provides causal evidence of
gains from trade without the need of factor prices as a metric.
[insert Table 1 here]
A striking feature of the gains in the labour categories, which are easily comparable because all
are measured in terms of days of work, is the large augmentation of female labour relative to skilled and
unskilled male labour. Depending on the sample year, the gain in female labour services is between two
to three times the total gain in male labour. This gain in female labour can be explained by Japan‟s intense
use of female labour in import-competing sectors such as yarn and cloth.
22
Another interesting feature of Panel C is the time series pattern of augmentation in the individual
factors. While the augmentation of skilled male followed a U-shaped path, the augmentation of the other
factors increased over the sample period. Between the mid-1860s and the mid-1870s, the augmentation of
unskilled male workers and land roughly doubled, and the augmentation of female workers and capital
almost tripled. This reveals increased specialization and increased gains from trade; it reflects generally
the adaptation of Japanese producers to world market conditions and improved matches between the
goods on offer by western merchants and the tastes of Japanese consumers.
An implicit requirement for assessing the static gains from trade is that the economy operates
under balanced trade. In a trade deficit year, the economy can be thought of as borrowing foreign factor
services and the factor content will overstate the static gains from trade. In a trade surplus year, the
economy can be thought of as lending domestic factor services and the factor content will understate the
static gains from trade. The Japanese economy experienced trade deficits in 1867 and over the period
1869-1875; trade surpluses occurred in 1865, 1868 and 1876.
The simplest procedure to correct for trade balances is to assume that Japanese preferences are
homothetic so that imports are scaled up in trade surplus years and scaled down in trade deficit years.
Hence, „adjusted‟ imports and exports satisfy the balanced trade condition. Panel D reports the resource
augmentation adjusted for trade imbalances. For years that saw trade surpluses such as 1865, 1868 and
1876, the adjustments to the factor augmentations are greater than one.32 Since Japan experienced trade
deficits during the other years, the trade adjusted augmentations are all smaller in Panel D than Panel C
for those years. Overall, the basic message from Panel C is preserved in Panel D. Even during years of
32
Adjustments to imports were made to ensure balanced trade in the share of goods (about 80 percent imports and
over 95 percent exports) for which data were available on factor usage. The adjustment factors (for imports) are 1.41
for 1865, 0.87 for 1867, 1.85 for 1868, 0.70 for 1869, 0.47 for 1870, 0.95 for 1871, 0.76 for 1872, 0.81 for 1873,
0.90 for 1874, 0.79 for 1875 and 1.46 for 1876.
23
trade deficits, all components of (Laug-L) remain positive, which implies that the revealed augmentation
in all factors is not caused by trade imbalances.
An attractive feature of our characterization is that the gain in factor i can be expressed as a
percentage increase in the economy‟s endowment Li of that factor.33 Censuses conducted in the mid1870s suggest that there were about 10.5 million male workers and about 8.5 female workers. Consistent
with the historical literature, children under 15 were not included in the labour force.34 The census results
also suggest that Japan was endowed with about 48 million tan of cultivated land.35 For the years 1869
and 1870, when poor harvests led to large imports of rice and beans, the augmentation of cultivated land
reached five per cent of Japan‟s endowment. For the post-crisis years of 1871-1876, the average was
roughly 3 per cent (see the final column of panels C and D). While the augmentation of (skilled and
unskilled) male labour was about 3% of the total labour force; the average augmentation of female labour
was about 7% per cent during 1871-1876.
3.3 Resource valuations and coefficient of resource utilization
Information on factor prices from Japan‟s autarky and free periods allows us to evaluate Japan‟s
trade-induced resource augmentation with the corresponding resource prices.36 This results in the
calculation of an overall welfare loss from the hypothetical overnight suspension of trade, captured by our
coefficients of resource utilization (6).
[insert Table 2 here]
33
It is important to remind ourselves that the augmentation of a specific factor of production is an aggregate gain to
the entire economy and has nothing to do with changes in the purchasing power of this factor that arise from trade.
We know from Stolper-Samuelson that some factors will gain and others will lose in terms of purchasing power.
34
Van Buren (1880, pp. 37 and 45) provides these estimates. Contemporary Japanese sources do not distinguish
between skilled and unskilled male labor. Consistent with historical sources, we assume a labor year of about 300
days of labor. The sources are insufficiently detailed to provide a reliable estimate of the capital stock.
35
One tan is about 0.25 acres.
36
For the remaining of the paper, all calculations are based on the trade-balance adjusted factor augmentation
reported in Panel D of Table 1.
24
Panel A in Table 2 provides the valuations when using Japan‟s resources prices during its autarky
period. The first two lines in Panel A report the factor content equivalent measure ΔLEV from equation (4)
in current ryō. The next line reports national income in autarky (the base years are 1851-1855). The
estimate is based upon a study of a prosperous feudal territory of Tokugawa Japan from 1842.37 The
values of autarky income have been adjusted to reflect the potential growth of the economy between the
autarky period (1855) and the sample years (1865 through 1876).38 The time series of the per capita
adjusted valuation suggests that the gains from trade roughly doubled between 1865 and 1876. The last
line reports the time series on the coefficient of resource utilization (6) evaluated at autarky prices. It is
interpreted as the counterfactual resource loss from the suspension of trade taking Japan‟s autarky period
as the reference point. The coefficient varies between 0.84 and 0.96 and averages 0.92 over the period. It
peaks during the two years of harvest failures and massive imports of rice and soybeans from China (1869
and 1870).
These estimates can now be compared to the Slutsky consumer expenditure measure of the gains
from trade in Bernhofen and Brown (2005), which are also based on a counterfactual exercise that takes
the autarky period as the reference point. Reassuringly, the comparable estimate reported in Bernhofen
and Brown (2005, Table 4) is about 9%, which is very close to the average factor income loss of 8%
reported in Panel A.39 The finding that the factor augmentation and the consumer expenditure
formulations yield quite similar results, in light of the fact that only the latter is based on the assumption
37
Nishikawa (1987) estimates that the feudal territory or han of Chōshū had a per capita income of about 2.53 ryō
in the early 1840s. With a growth rate of 0.4 percent, that would be about 2.67 by 1855. This han had a higher share
of its population (about 15 percent) in the secondary and tertiary sectors than most of Japan. Household income in
these sectors was about 2.5 times incomes in agriculture. If we assume a more realistic share of 10 percent outside of
agriculture, the per capita income would be about 2.52. This estimate is used for the calculations of national income
in the autarky period.
38
Growth of the economy from 1855 to the trade period would have increased the production potential of the
economy. These calculations assume that per capita autarky factor income grew 0.4% per year. Nishikawa (1987, p.
327) suggests such a growth rate was a reasonable estimate for mid-century.
39
The earlier paper did not make adjustments for trade deficits or surpluses.
25
that the weak axiom of revealed preference holds on the aggregate, can be interpreted as „suggestive
evidence‟ for the empirical validity of this axiom in this empirical environment.
Panel B of Table 2 presents the calculations of the compensating variation measure of factor
gains ΔLCV from (5), which gives the change in the economy‟s total factor income necessary to fully
compensate for the elimination of the factor augmentation ( Laug –L) brought about by trade. The
reference point of this counterfactual exercise is the free trade period and the advantage of the factor
augmentation formulation is that the calculation of the compensation only requires data observed in the
trade equilibrium. This is in stark contrast to the Slutsky compensation measure (2), which requires
consumption data under autarky and trade.40
The change in factor income is evaluated at free trade factor prices (wt), which are from the
period 1875-1879. Panel B gives ΔLCV in millions of yen.41 The time series confirms the finding from
Panel A that the aggregate gains more than doubled between the beginning and the end of the sample
period. Estimates of national income are the values for 1878-1882 found in Okawa (1957, Table 1), which
have been adjusted downward under the assumption of a growth rate in per capita income of 0.4% over
the first period of open trade. The corresponding coefficient of resource utilization varies between 0.88
and 0.96 and takes its minimum in the end year of the sample period. The average value is also 0.92 for
the entire period. The slightly higher magnitudes of the coefficient in Panel B can be explained by the free
trade period being the reference point for the hypothetical suspension of trade, which corresponds to a
higher base production capacity than the one in Panel A.42 Recalling from propositions 1 and 2 that (4)
40
See Bernhofen and Brown (2004, p.212) for a detailed discussion of why (2) cannot be approximated by data on
prices and trade flows.
41
The underlying assumption is that growth rate of per capita GDP was 0.4% of the period 1865-1876.
42
The gains from trade can be thought as „capturing movements along the economy‟s PPF‟ which become
„relatively smaller‟ as the PPF moves further away from the origin. The underlying assumption of the analysis is that
the economy‟s actual growth path is invariant to the static gains from trade. A relaxation of this assumption is
beyond the theoretical scope of this static theoretical framework.
26
and (5) are upper and lower bounds of the expenditure measures (2) and (1), the findings in Panels A and
B suggest that the different welfare measures give quantitatively quite similar results. In summary, the
average static welfare benefit from trade was about 8% in terms of the economy‟s overall productive
capacity.
4. Conclusion
It is quite well known that the factor content of trade is a fruitful device for higher dimensional
formulations of the Heckscher-Ohlin theorem.43 As a result, it has inspired a voluminous empirical
literature estimating patterns of international specialization and linking them to various theoretical
specifications. To the best of our knowledge, this paper is the first to use the factor content of trade as an
analytical device for a new theoretical formulation of the gains from trade and then applies it to a unique
new data set.
We show that an economy's factor content of trade embodies all the relevant information about a
factor augmentation equivalent to trade which formalizes the gains from trade as originally characterized
in the eighteenth century. Viner (1937, chapter 8, p. 9 ) has pointed out that "...many of the classical
economists, before and after the formulation of the doctrine of comparative costs, resorted to this
eighteenth-century rule as a test of the existence of the gains from trade (and that) Ricardo incorporated it
in his (famous 1817) formulation of the doctrine of comparative costs”. A main advantage of this
formulation is that the gains can be tested without the imposition of a supportive auxiliary hypothesis on
aggregate consumer behaviour, like the weak axiom of revealed preference. This has the important
implication that the gains from trade are subject to empirical refutation a la Popper, without qualifications
about the testing of joint hypotheses raised by Duhem-Quine.44
43
See Feenstra (2004) and Bernhofen (2011) for recent surveys of the factor content literature.
44
The Duhem-Quine thesis raises concerns about the refutability of single hypotheses since hypotheses are often
formulated in conjunction with supportive hypotheses which are assumed to be true. In our context, a test of the
27
Applying our formulation to a unique data set on 19th century Japan, we provide causal evidence
of the existence of the gains from trade expressed in an augmentation of all factors of production in all
sample years. In addition, we also show that our theoretical approach provides insights into the deeper
determinants of the sources and magnitudes of the aggregate gains from trade. Although there are distinct
advantages to apply our gains from trade formulation to the case of 19th century Japan, the fact that our
approach does not require autarky data should be a stimulus for future applications in different empirical
settings.
gains from trade in its revealed preference formulation is always a joint test of the gains from trade and the weak
axiom of revealed preference. SeeCross (1982) for a good discussion of these concerns in the context of testing
theories of macroeconomics.
28
Figure 1: Expenditure measures of the gains from trade
good 2
ΔICV
pt
Ct
Ca
pa
ΔIEV
good 1
29
Figure 2: Factor augmentation equivalent to trade
good 2
pt
PPF(Laug)
Ct
Ca
T
PPF(L)
M2
pa
Yt
X1
good 1
30
Figure 3: Factor augmentation measures of the gains from trade
factor 2
slope= - w1j/w2j ; (j=a or t)
Laug
II
I
AmM
L
L2
gains in units of factor 1
AxX
III
IV
factor 1
L1
31
References
Arkolakis, C., A. Costinot, et al. (2009). "New Trade Models, Same Old Gains?" American Economic
Review 102(1): 94-130.
Bavier, E. d. (1874). La sériciculture : le commerce des soies et des graines et l'industrie de la soie au
Japon. Lyon and Milan, H. Georg Du Molard frères.
Bernheim, B. D. and A. Rangel (2007). "Toward Choice-Theoretic Foundations for Behavioral Welfare
Economics." American Economic Review 97(2): 464-470.
Bernheim, B. D. and A. Rangel (2009). "Beyond Revealed Preference: Choice-Theoretic Foundations for
Behavioral Welfare Economics." Quarterly Journal of Economics 124(1): 51-104.
Bernhofen, D. M. (2009). "Predicting the pattern of international trade in the neoclassical model: a
synthesis." Economic Theory 41: 5-21.
Bernhofen, D. M. (2011). The empirics of general equilibrium trade theory. In D. M. Bernhofen, R.
Falvey, D. Greenaway and U. Kreickemeier, ed Palgrave Handbook of International Trade.
Basingstoke, United Kingdom, Palgrave MacMillan: 88-118.
Bernhofen, D. M. and J. C. Brown (2004). "A Direct Test of the Theory of Comparative Advantage: The
Case of Japan." Journal of Political Economy 112(1): 48-67.
Bernhofen, D. M. and J. C. Brown (2005). "An Empirical Assessment of the Comparative Advantage
Gains from Trade: Evidence from Japan." American Economic Review 95(1): 208-225.
Burstein, A. and J. Vogel (2011). Factor Prices and International Trade: A Unifying Perspective,
National Bureau of Economic Research, Inc, NBER Working Papers: 16904.
Chetty, R. (2009). "Sufficient Statistics for Welfare Analysis: A Bridge between Structural and ReducedForm Methods." Annual Review of Economics 1(1): 451-487.
Chō, Y., K. Shōda, et al. (1979). Meiji chūki sangyō undō shiryō. Tōkyō, Nihon Keizai Hyōronsha.
Cross, R. (1982). "The Duhem-Quine Thesis, Lakatos and the Appraisal of Theories in Macroeconomics."
Economic Journal 92(366): 320-340.
Deardorff, A. V. (1982). "The General Validity of the Heckscher-Ohlin Theorem." American Economic
Review 72(4): 683-694.
Deardorff, A. V. (2000). "Factor Prices and the Factor Content of Trade Revisited: What's the Use?"
Journal of International Economics 50(1): 73-90.
Deardorff, A. V. and R. W. Staiger (1988). "An Interpretation of the Factor Content of Trade." Journal of
International Economics 24(1/2): 93-107.
Deaton, A. (1979). "The Distance Function in Consumer Behaviour with Applications to Index Numbers
and Optimal Taxation." Review of Economic Studies 46(3): 391-405.
Debreu, G. (1951). "The Coefficient of Resource Utilization." Econometrica 19(3): 273-292.
Feenstra, R. C. (2004). Advanced International Trade : Theory and Evidence. New Jersey, University
Presses of California, Columbia and Princeton.
Ichikawa, T. (1996). Nihon nōson kōgyōshi kenkyū : Kiryū Ashikaga orimonogyō no bunseki. Tōkyō,
Bunshindō.
Kemp, M. (1962). "The gain from international trade." Economic Journal 72(288): 803-819.
32
Le Gendre, C. W. (1878). Progressive Japan, a study of the political and social needs of the empire. New
York, Yokohama,C. Lévy.
Lyman, B. S. (1879). Geological Survey of Japan: Reports of Progress for 1878 and 1879. Tookei, Public
Works Department.
Maneschi, A. (2004). "The True Meaning of David Ricardo's Four Magic Numbers." Journal of
International Economics 62(2): 433-443.
Neary, J. P. and A. G. Schweinberger (1986). "Factor Content Functions and the Theory of International
Trade." Review of Economic Studies 53(3): 421-432.
Nishikawa, S. (1987). "The Economy of Choshu on the Eve of Industrialization." Economic Studies
Quarterly 38(4): 323-337.
Okawa, K. (1957). The growth rate of the Japanese economy since 1878. Tokyo, Kinokuniya Bookstore
Co.
Porter, R. P. and National Association of Manufacturers (U.S.) (1898). Commerce and industries of
Japan : a report of investigations conducted by Robert P. Porter. Philadelphia, Bureau of
Publicity National Association of Manufacturers.
Ricardo, D. (1817). On the principles of political economy and taxation. London, John Murray.
Ruffin, R. J. (2002). "David Ricardo's Discovery of Comparative Advantage." History of Political
Economy 34(4): 727-748.
Saitō, O. (1998). Chingin to rōdō to seikatsu suijun : Nihon keizaishi ni okeru 18--20-seiki. Tōkyō,
Iwanami Shoten.
Saitō, O. and T. Settsu (2006). Money, credit and Smithian growth in Tokugawa Japan. Tokyo,
Hitotsubashi University.
Samuelson, P. A. (1938). "A note on the pure theory of consumer's behavior." Economica 5(17): 61-71.
Samuelson, P. A. (1939). "The gains from international trade." Canadian Journal of Economics and
Political Science 5(2): 195-205.
Samuelson, P. A. (1962). "The gains from trade once again." The Economic Journal 72(288): 820-829.
Samuelson, P. A. (1969). The way of an economist. In P. A. Samuelson, ed International Economic
Relations: Proceedings of the Third Congress of the International Economic Association.
London, MacMillan: 1-11.
Shinbo, H. (1978). Kinsei no bukka to keizai hatten : zen kōgyōka shakai e no sūryōteki sekkin. Tōkyō,
Tōyō Keizai Shinpōsha.
Sraffa, P. (1930). "An alleged correction of Ricardo." Quarterly Journal of Economics 44: 539-545.
Sugden, R. (2004). "The Opportunity Criterion: Consumer Sovereignty without the Assumption of
Coherent Preferences." American Economic Review 94(4): 1014-1033.
Tamura, H. (2004). Fasshon no shakai keizaishi : zairai orimonogyō no gijutsu kakushin to ryūkō shijō.
Tōkyō, Nihon Keizai Hyōronsha.
Tanimoto, M. (1998). Nihon ni okeru zairaiteki keizai hatten to orimonogyō : shijō keisei to kazoku
keizai. Nagoya-shi, Nagoya Daigaku Shuppankai.
Van Buren, T. B. (1880). Labor in Japan. Reports from the Consuls of the United States on teh
Commerce, Manufactures, etc. of their Consular Districts. Washington, DC, United States
Department of State. 2: 34-57.
33
Viner, J. (1937). Studies in the theory of international trade. New York, London, Harper & brothers.
Woodland, A. D. (1980). "Direct and Indirect Trade Utility Functions." Review of Economic Studies
47(5): 907-926.
34
Table 1: Japan's revealed factor augmentation: 1865, 1867-1876
Aan
1865
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
Panel A: Factor Imports: AmM
Male skilled (mm days)
31
23
15
16
22
24
24
30
25
32
29
Male unskilled (mm days)
60
70
48
68
120
115
99
116
100
137
117
Female (mm days)
63
93
80
98
177
184
170
179
194
210
209
Capital (thousands of ryō)
1,151 1,720 1,266 1,572 2,613 2,725 2,542 2,905 2,762 3,698 3,203
Land (thousands of tan)
1,107 1,340
870 1,542 2,852 2,486 1,781 2,083 1,743 2,399 2,026
x
Panel B: Factor Exports: A X
Male skilled (mm days)
6
6
5
4
6
9
8
8
9
10
11
Male unskilled (mm days)
34
20
28
19
21
35
29
33
31
34
51
Female (mm of days)
10
6
9
6
7
11
8
10
10
11
16
Capital (thousands of ryō)
748
472
626
453
540
846
718
793
843
925 1,151
Land (thousands of tan)
662
404
564
394
443
707
566
678
693
754 1,094
Panel C: Factor augmentation: ΔL=AmM-AxX
Average of
ΔLi/ Li:
Male skilled (mm days)
25
17
10
12
17
15
16
22
16
23
18
3.1%
Male unskilled (mm days)
26
50
20
49
100
80
70
83
69
103
66
7.1
Female (mm days)
52
86
71
92
171
172
161
169
185
199
194
Capital (thousands of ryō)
403 1248
640 1119 2073 1879 1825 2112 1919 2773 2052
2.8
Land (thousands of tan)
445
936
305 1148 2409 1779 1215 1405 1051 1646
932
Panel D: Factor augmentation: ΔL, adjusted for trade imbalances
Average of
ΔLi/ Li:
Male skilled (mm days)
38
14
22
7
5
14
10
16
13
16
31
2.8%
Male unskilled (mm days)
50
41
61
28
36
74
47
61
59
73
120
6.7
Female (mm days)
78
74
140
62
76
164
121
135
165
154
291
Capital (thousands of ryō)
875 1020 1715
642
679 1745 1220 1571 1642 1979 3537
2.6
Land (thousands of tan)
899
759 1045
680
888 1657
792 1017
876 1131 1872
}
35
Source: For the procedure used to calculate the estimated factor flows, please see the text.
Notes: Information on the Japanese endowments of male and female labor and land are from the censuses of 1875 reported in Van Buren (1880,
pp. 37 and 45). The net imports as a share of the endowment, ΔLi/ Li, is for the average for each factor from 1871 through 1876.
36
Table 2: Evaluating the resource augmentation and the loss of resource use from the suspension of trade
1865
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
Panel A: Equivalent variation
6.67
ΔLEV (in millions of ryō)
a
79.31
w L (in millions of ryō) †
a
a
85.98
w L+w F
Debreu's RUC (
0.92
5.06
79.95
85.00
0.94
8.27
80.27
88.53
0.91
3.66
80.59
84.25
0.96
4.27
80.91
85.17
0.95
9.34
81.23
90.58
0.90
6.14
81.56
87.69
0.93
7.71
81.88
89.59
0.91
7.99
82.21
90.20
0.91
8.90
82.54
91.44
0.90
15.89
82.87
98.76
0.84
Panel B: Compensating variation
31.13 24.40 40.34 17.98 21.24 46.19 30.76 38.05 40.25 43.96 78.61
ΔLCV (in millions of yen)
t
359.57 388.92 404.47 420.65 437.48 454.98 473.18 492.10 511.79 532.26 553.55
w L (in millions of yen) ‡
t
t
390.71 413.31 444.81 438.63 458.72 501.17 503.93 530.15 552.04 576.22 632.16
w L+w F
Debreu's RUC (
0.92
0.94
0.91
0.96
0.95
0.91
0.94
0.93
0.93
0.92
0.88
†Adjusted for growth in production possibilities from 1855 to the relevant year at a rate of 0.4 percent per year.
‡Adjusted for growth in real GDP per capita to 1880 from the relevant year at a rate of 0.4 percent per year.
Source: ΔLEV : the inner product of the net imports of factors from Panel D of Table 1 and the vector of autarky factor prices.
ΔLCV: the inner product of the net imports of factors from Panel D of Table 1 and the vector of open trade factor prices.
Notes: The ryō is the currency used in Japan during autarky. The yen was introduced in 1871 to replace the (paper) ryō at a ratio of one to one.
37